Question

Aratati ca numarul 29^2017 se poate scrie ca o suma de doua patrate perfecte

Answer 1

$29^{2017}=29*29^{2016}=$

$=(25+4)*(29^{1008})^{2}=$

$=(5^{2}+2^{2})*(29^{1008})^{2}=$

$=5^{2}*(29^{1008})^{2}+2^{2}*(29^{1008})^{2}=$

$=(5*29^{1008})^{2}+(2*29^{1008})^2$